Such a pressure amplifier is known, for example, from U.S. Pat. No. 6,866,485 B2. The force transmitting means is formed by a stepped piston. The stepped piston has a larger low pressure area in the low pressure chamber and a smaller high pressure area in the high pressure chamber. When the low pressure chamber is supplied with a fluid under pressure a force is generated shifting the piston in a direction to decrease the volume of the high pressure chamber. The force is basically the product of the low pressure area and the pressure in the low pressure chamber. This force leads to a pressure in the high pressure chamber which is basically the force divided by the high pressure area.